"Next week’s special congressional election in southwestern Pennsylvania will test whether, deep in Trump country, union support can help elect a Democrat running on a middle-class economic agenda. A victory would remind Democrats of the electoral power of organized labor. Even though it has relied on unions’ electoral muscle for nearly a century, the party has often failed to shore up labor’s diminishing strength. Our research demonstrates what an enormous electoral mistake that has been.

Political analysts have long argued that dwindling union power would be bad for Democrats. The conservative strategist Grover Norquist, for instance, has speculated that the decline of labor in recent years could mean that Republicans (and President Trump) may continue to win big despite Mr. Trump’s unpopularity. But there were not reliable estimates of the size of that effect on elections.

We have quantified the electoral effects of one kind of anti-union law, commonly called “right to work” legislation. Those bills allow workers to opt out of paying fees to a union at their workplace — even if those workers benefit from union bargaining and protections. The results are ugly for Democrats and for the working class.

We looked at how right-to-work laws shaped elections from 1980 through 2016. We compared pairs of counties, one in a state that passed a right-to-work law and the other just across the border in a state that didn’t. Even if right-to-work and non-right-to-work states are quite different, bordering counties in many states tend to have similar economic, demographic and political trends. Our approach, which isolates the changes that show up only when right-to-work laws are passed, holds up even when we account for other state-level legislation passed at the same time as right-to-work bills, including voter ID laws and other common pieces of conservative legislation.

A study of adjoining counties across state borders found that Democrats performed, in presidential elections, about the same on both sides — until one state adopted right-to-work laws. Then the county vote trends diverged.

When right-to-work laws are in place, Democrats up and down the ballot do worse. In presidential elections, we estimate that these laws cost Democratic candidates two to five percentage points in right-to-work counties. Voter turnout also dropped by approximately two points. That is not trivial, especially considering that Hillary Clinton lost Michigan and Wisconsin in 2016 — two relatively recent right-to-work states — by less than one percentage point each. We find similar effects at other levels of government. Democrats, for instance, are less likely to win state legislative seats after the passage of right-to-work laws.

With a weaker labor movement, it’s not just Democratic electoral prospects that suffer. The working class loses, too. We find that the number of state legislators who had previously worked in blue-collar jobs drops sharply after right-to-work goes into effect. These politicians tend to strongly support economic policies preferred by working-class Americans, like a higher minimum wage and a stronger safety net. Right-to-work laws thus undercut political representation for working-class people, a group that is disproportionately nonwhite, and reduce the legislative voice for progressive economic policies."